The batteries would not expire rather quickly. Battery life is often rated in number of charge cycles, which if you aren't using it much, would be experiencing fewer charge cycles.
The power you could get on a camper from solar isn't miniscule. It's insufficient on a vehicle that has a tiny roof and often parks indoors, but a camper has a huge mostly flat top and generally stays outside when in use. Some of those trailers you could fit 20 full size panels on. That's the same number as I have on my house.